\theoremstyle{definition}
\swapnumbers
\newtheorem{Definition}{Definition}[section]
\newtheorem{Corollary}{Definition}[Corollary]
\newtheorem{Remark}[Definition]{Remark}
\newtheorem{Theorem}[Definition]{Theorem}
\newtheorem{Lemma}[Definition]{Lemma}
\newtheorem{Satz}[Definition]{Theorem}
\newtheorem{Proposition}[Definition]{Proposition}
\newtheorem{Conjecture}[Definition]{Conjecture}
\newtheorem{Example}[Definition]{Example}
\newtheorem*{DefinitionUnnumbered}{Definition}
\newtheorem*{TheoremUnnumbered}{Theorem}
\newtheorem{Bemerkung}{Bemerkung}
\newtheorem{Korollar}{Korollar}
\newtheorem{Beispiel}{Beispiel}
\newtheorem{Beispiele}[Beispiel]{Beispiele}
\newtheorem*{Beweis}{Proof}
\newtheorem*{Proof}{Proof}

\renewcommand{\phi}{\varphi}

%\newtheorem*{proof}{Proof}
\newcommand{\ra}{\rightarrow}
\newcommand{\RA}{\Rightarrow}
\newcommand{\barf}{f_0}
\newcommand{\xbar}{x_0}
\newcommand{\ETL}{\text{ETL}}

\newcommand{\mapstoreverse}{\leftarrow\joinrel\mapstochar}

\newcommand{\VPALR}{\text{VPAL$_r$}}
\newcommand{\VPALL}{\text{VPAL$_l$}}
\newcommand{\VPALF}{\text{VPAL$_f$}}
\newcommand{\VPAL}{\text{VPAL}}

\newcommand{\ETLR}{\text{ETL$_r$}}
\newcommand{\ETLL}{\text{ETL$_l$}}
\newcommand{\ETLF}{\text{ETL$_f$}}

\newcommand{\AUFO}{\text{AUFO}}
\newcommand{\AUCARET}{\text{AUCARET}}
\newcommand{\ECARET}{\text{ECARET}}
\newcommand{\notatStep}[1]{\phi_{#1 \text{ not at step}}}
\newcommand{\inftySteps}[1]{\phi_{#1~\text{at $\infty$ steps}}}
\newcommand{\colorfunction}{\mathfrak{C}}
\newcommand{\dcup}{\ensuremath{\mathaccent\cdot\cup}}
\newcommand{\xt}{\overline{x}}
\newcommand{\yt}{\overline{y}}
\newcommand{\muGF}{\mu\mathsf{GF}}
\newcommand{\AAA}{\mathfrak{A}}
\newcommand{\AT}{{\cal A}}
\newcommand{\GG}{{\cal G}}
\newcommand{\TB}{{\cal T}}
\newcommand{\FP}{{\mathrm {FP}}}
\newcommand{\cd}{\cdot}
\newcommand{\pp}{p}
\newcommand{\NN}{\mathbb{N}}
\newcommand{\HH}{\mathbb{H}}
\newcommand{\KK}{\mathbb{K}}
\newcommand{\RR}{\mathbb{R}}
\newcommand{\CC}{\mathcal{C}}
\newcommand{\CCC}{\mathbb{C}}
\newcommand{\BB}{\mathbb{B}}
\newcommand{\OO}{\mathbb{O}}
\newcommand{\DD}{\mathcal{D}}

\newcommand{\QQ}{\mathbb{Q}}
\newcommand{\Inf}[1]{Inf(#1)}
\newcommand{\Occ}[1]{Occ(#1)}
\newcommand{\MSOSignatur}{(<,(P_a)_{a\in \Sigma},\mu, Call, Ret)}
\newcommand{\ZZ}{\mathbb{Z}}
\newcommand{\RRR}{\mathfrak{R}}
\newcommand{\powerset}[1]{\mathfrak{P}(#1)}
\newcommand{\comment}[1]{{\color{red} #1}}
\newcommand{\mathsc}[1]{\text{\textsc{#1}}}
\newcommand{\exptime}{\mathsc{Exptime}}
\newcommand{\iso}{\xrightarrow{\sim}}
\newcommand{\down}{\!\!\downarrow}
\newcommand{\kommentar}[1]{}
\newcommand{\universal}[6]{

$$\xymatrix{
#1 \ar[dr]_{ #4 } \ar[r]^{ #5 } & #2 \ar@{.>}[d]^{ #6 }\\
&  #3}$$

}

\newcommand{\factorizes}[6]{

$$\xymatrix{
#1 \ar[dr]_{ #4 } \ar[r]^{ #5 } & #3 \\
&  #2\ar@{.>}[u]_{ #6 }}$$

}


%FOR XY- Pic
\newdir^{ (}{{}*!/-5pt/@^{(}}